Here's how to determine the net ionic equation for the reaction between barium chloride (BaCl₂) and lead(II) acetate (Pb(C₂H₃O₂)₂):

1. Write the balanced molecular equation:

BaCl₂(aq) + Pb(C₂H₃O₂)₂(aq) → Ba(C₂H₃O₂)₂(aq) + PbCl₂(s)

2. Write the complete ionic equation:

This involves breaking down all soluble ionic compounds into their respective ions:

Ba²⁺(aq) + 2Cl⁻(aq) + Pb²⁺(aq) + 2C₂H₃O₂⁻(aq) → Ba²⁺(aq) + 2C₂H₃O₂⁻(aq) + PbCl₂(s)

3. Identify the spectator ions:

Spectator ions are those that appear on both sides of the equation and do not participate in the reaction. In this case, the spectator ions are Ba²⁺(aq) and C₂H₃O₂⁻(aq).

4. Write the net ionic equation:

This is the equation that only includes the ions that directly participate in the reaction:

Pb²⁺(aq) + 2Cl⁻(aq) → PbCl₂(s)

Therefore, the net ionic equation for the reaction between barium chloride and lead acetate is Pb²⁺(aq) + 2Cl⁻(aq) → PbCl₂(s).